TSTP Solution File: GRP382-1 by Gandalf---c-2.6
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- Process Solution
%------------------------------------------------------------------------------
% File : Gandalf---c-2.6
% Problem : GRP382-1 : TPTP v3.4.2. Released v2.5.0.
% Transfm : add_equality:r
% Format : otter:hypothesis:set(auto),clear(print_given)
% Command : gandalf-wrapper -time %d %s
% Computer : art01.cs.miami.edu
% Model : i686 unknown
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1000MB
% OS : Linux 2.4.22-21mdk-i686-up-4GB
% CPULimit : 600s
% Result : Unsatisfiable 299.0s
% Output : Assurance 299.0s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
%
% Gandalf c-2.6 r1 starting to prove: /home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP382-1+eq_r.in
% Using automatic strategy selection.
% Time limit in seconds: 600
%
% prove-all-passes started
%
% detected problem class: peq
%
% strategies selected:
% (hyper 30 #f 3 33)
% (binary-unit 12 #f)
% (binary-unit-uniteq 12 #f)
% (binary-posweight-kb-big-order 60 #f 3 33)
% (binary-posweight-lex-big-order 30 #f 3 33)
% (binary 30 #t)
% (binary-posweight-kb-big-order 156 #f)
% (binary-posweight-lex-big-order 102 #f)
% (binary-posweight-firstpref-order 60 #f)
% (binary-order 30 #f)
% (binary-posweight-kb-small-order 48 #f)
% (binary-posweight-lex-small-order 30 #f)
%
%
% SOS clause
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% was split for some strategies as:
% -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11).
% -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12).
% -equal(inverse(sk_c12),sk_c11).
% -equal(multiply(sk_c11,sk_c10),sk_c12).
%
% Starting a split proof attempt with 7 components.
%
% Split component 1 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X3),X1) | -equal(inverse(X2),X3) | -equal(multiply(X2,X1),X3).
% END OF PROOFPART
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092)
%
%
% START OF PROOF
% 380835 [] equal(multiply(identity,X),X).
% 380836 [] equal(multiply(inverse(X),X),identity).
% 380837 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 380908 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,X),sk_c12) | -equal(multiply(Z,X),U) | -equal(inverse(Z),U) | -equal(inverse(U),X) | -equal(inverse(Y),X).
% 380909 [] -equal(multiply(X,Y),Z) | -equal(inverse(X),Z) | -equal(inverse(Z),Y) | $spltprd1($spltcnst97,Y).
% 380910 [] -equal(multiply(X,Y),sk_c12) | -equal(inverse(X),Y) | $spltprd1($spltcnst98,Y).
% 380911 [] -equal(multiply(X,sk_c11),sk_c12) | $spltprd1($spltcnst99,X).
% 380912 [] -$spltprd1($spltcnst98,X) | -$spltprd1($spltcnst97,X) | -$spltprd1($spltcnst99,X).
% 380923 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c2),sk_c3).
% 380924 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c7),sk_c9).
% 380925 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 380926 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c2),sk_c3).
% 380927 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 380928 [?] ?
% 380933 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 380934 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 380935 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 380936 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 380937 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 380938 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 380943 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c8,sk_c9),sk_c7).
% 380944 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 380945 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 380946 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c9,sk_c11),sk_c12).
% 380947 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 380948 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 380953 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c1),sk_c12).
% 380954 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 380955 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 380956 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c1),sk_c12).
% 380957 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 380958 [?] ?
% 380973 [] equal(multiply(sk_c8,sk_c9),sk_c7) | equal(inverse(sk_c12),sk_c11).
% 380974 [] equal(inverse(sk_c12),sk_c11) | equal(inverse(sk_c7),sk_c9).
% 380975 [] equal(inverse(sk_c12),sk_c11) | equal(inverse(sk_c8),sk_c7).
% 380976 [] equal(multiply(sk_c9,sk_c11),sk_c12) | equal(inverse(sk_c12),sk_c11).
% 380977 [] equal(inverse(sk_c12),sk_c11) | equal(inverse(sk_c6),sk_c9).
% 380978 [?] ?
% 381049 [hyper:380910,380927,binarycut:380928] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst98,sk_c9).
% 381137 [hyper:380910,380957,binarycut:380958] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst98,sk_c9).
% 381225 [hyper:380910,380977,binarycut:380978] equal(inverse(sk_c12),sk_c11) | $spltprd1($spltcnst98,sk_c9).
% 381367 [hyper:380909,380923,380924,380925] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst97,sk_c9).
% 381398 [hyper:380911,380926] equal(inverse(sk_c2),sk_c3) | $spltprd1($spltcnst99,sk_c9).
% 381409 [hyper:380912,381398,381367,381049] equal(inverse(sk_c2),sk_c3).
% 381416 [para:381409.1.1,380836.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 381779 [hyper:380909,380953,380954,380955] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst97,sk_c9).
% 381883 [hyper:380911,380956] equal(inverse(sk_c1),sk_c12) | $spltprd1($spltcnst99,sk_c9).
% 381931 [hyper:380912,381883,381779,381137] equal(inverse(sk_c1),sk_c12).
% 381975 [para:381931.1.1,380836.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 382156 [hyper:380909,380973,380974,380975] equal(inverse(sk_c12),sk_c11) | $spltprd1($spltcnst97,sk_c9).
% 382191 [hyper:380911,380976] equal(inverse(sk_c12),sk_c11) | $spltprd1($spltcnst99,sk_c9).
% 382207 [hyper:380912,382191,382156,381225] equal(inverse(sk_c12),sk_c11).
% 382219 [para:382207.1.1,380836.1.1.1] equal(multiply(sk_c11,sk_c12),identity).
% 382628 [hyper:380908,380938,380936,380937,380934,380933,380935] equal(multiply(sk_c2,sk_c3),sk_c11).
% 382786 [hyper:380908,380948,380946,380947,380944,380943,380945] equal(multiply(sk_c1,sk_c11),sk_c12).
% 382904 [para:380836.1.1,380837.1.1.1,demod:380835] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 382905 [para:381416.1.1,380837.1.1.1,demod:380835] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 382906 [para:381975.1.1,380837.1.1.1,demod:380835] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 382907 [para:382219.1.1,380837.1.1.1,demod:380835] equal(X,multiply(sk_c11,multiply(sk_c12,X))).
% 382946 [para:382786.1.1,382906.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 382956 [para:381975.1.1,382907.1.2.2] equal(sk_c1,multiply(sk_c11,identity)).
% 382965 [para:382906.1.2,382907.1.2.2] equal(multiply(sk_c1,X),multiply(sk_c11,X)).
% 382973 [para:382965.1.2,382956.1.2] equal(sk_c1,multiply(sk_c1,identity)).
% 383085 [para:382905.1.2,382904.1.2.2] equal(multiply(sk_c2,X),multiply(inverse(sk_c3),X)).
% 383112 [para:383085.1.2,380836.1.1,demod:382628] equal(sk_c11,identity).
% 383118 [para:383112.1.1,382219.1.1.1,demod:380835] equal(sk_c12,identity).
% 383119 [para:383112.1.1,382786.1.1.2,demod:382973] equal(sk_c1,sk_c12).
% 383123 [para:383112.1.1,382907.1.2.1,demod:380835] equal(X,multiply(sk_c12,X)).
% 383129 [para:383118.1.1,382207.1.1.1] equal(inverse(identity),sk_c11).
% 383131 [para:383118.1.1,382946.1.2.1,demod:380835] equal(sk_c11,sk_c12).
% 383134 [para:383119.1.2,382207.1.1.1,demod:381931] equal(sk_c12,sk_c11).
% 383161 [para:383131.1.2,382207.1.1.1] equal(inverse(sk_c11),sk_c11).
% 383194 [hyper:380908,383129,380835,demod:383161,380835,demod:383129,383123,cut:383131,cut:383131,cut:383131,cut:383134] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 2 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103)
%
%
% START OF PROOF
% 383195 [] equal(multiply(identity,X),X).
% 383196 [] equal(multiply(inverse(X),X),identity).
% 383197 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 383198 [] -equal(multiply(X,sk_c11),sk_c10) | -equal(inverse(X),sk_c11).
% 383205 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 383206 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 383215 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c5),sk_c11).
% 383216 [?] ?
% 383225 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 383226 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 383235 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c5),sk_c11).
% 383236 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 383245 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c5),sk_c11).
% 383246 [?] ?
% 383255 [] equal(multiply(sk_c11,sk_c10),sk_c12) | equal(inverse(sk_c5),sk_c11).
% 383256 [] equal(multiply(sk_c11,sk_c10),sk_c12) | equal(multiply(sk_c5,sk_c11),sk_c10).
% 383265 [] equal(inverse(sk_c12),sk_c11) | equal(inverse(sk_c5),sk_c11).
% 383266 [?] ?
% 383275 [hyper:383198,383215,binarycut:383216] equal(inverse(sk_c2),sk_c3).
% 383276 [para:383275.1.1,383196.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 383283 [hyper:383198,383245,binarycut:383246] equal(inverse(sk_c1),sk_c12).
% 383284 [para:383283.1.1,383196.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 383298 [hyper:383198,383265,binarycut:383266] equal(inverse(sk_c12),sk_c11).
% 383301 [para:383298.1.1,383196.1.1.1] equal(multiply(sk_c11,sk_c12),identity).
% 383326 [hyper:383198,383206,383205] equal(multiply(sk_c3,sk_c12),sk_c11).
% 383340 [hyper:383198,383226,383225] equal(multiply(sk_c2,sk_c3),sk_c11).
% 383346 [hyper:383198,383236,383235] equal(multiply(sk_c1,sk_c11),sk_c12).
% 383352 [hyper:383198,383256,383255] equal(multiply(sk_c11,sk_c10),sk_c12).
% 383353 [para:383196.1.1,383197.1.1.1,demod:383195] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 383354 [para:383276.1.1,383197.1.1.1,demod:383195] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 383355 [para:383284.1.1,383197.1.1.1,demod:383195] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 383357 [para:383326.1.1,383197.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c3,multiply(sk_c12,X))).
% 383360 [para:383352.1.1,383197.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c11,multiply(sk_c10,X))).
% 383361 [para:383340.1.1,383354.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c11)).
% 383363 [para:383346.1.1,383355.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 383364 [para:383363.1.2,383197.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c12,multiply(sk_c12,X))).
% 383368 [para:383301.1.1,383353.1.2.2] equal(sk_c12,multiply(inverse(sk_c11),identity)).
% 383370 [para:383352.1.1,383353.1.2.2] equal(sk_c10,multiply(inverse(sk_c11),sk_c12)).
% 383372 [para:383355.1.2,383353.1.2.2,demod:383298] equal(multiply(sk_c1,X),multiply(sk_c11,X)).
% 383374 [para:383368.1.2,383197.1.1.1,demod:383195] equal(multiply(sk_c12,X),multiply(inverse(sk_c11),X)).
% 383376 [para:383370.1.2,383197.1.1.1,demod:383372,383364,383374] equal(multiply(sk_c10,X),multiply(sk_c1,X)).
% 383386 [para:383355.1.2,383357.1.2.2,demod:383360,383376] equal(multiply(sk_c12,X),multiply(sk_c3,X)).
% 383387 [para:383363.1.2,383357.1.2.2,demod:383361,383301] equal(identity,sk_c3).
% 383389 [para:383387.1.2,383276.1.1.1,demod:383195] equal(sk_c2,identity).
% 383390 [para:383387.1.2,383326.1.1.1,demod:383195] equal(sk_c12,sk_c11).
% 383394 [para:383387.1.2,383357.1.2.1,demod:383195,383386,383376,383372] equal(multiply(sk_c10,X),multiply(sk_c3,X)).
% 383397 [para:383389.1.1,383354.1.2.2.1,demod:383394,383195] equal(X,multiply(sk_c10,X)).
% 383398 [para:383390.1.1,383298.1.1.1] equal(inverse(sk_c11),sk_c11).
% 383399 [para:383390.1.1,383301.1.1.2,demod:383346,383372] equal(sk_c12,identity).
% 383402 [para:383390.1.1,383370.1.2.2,demod:383346,383372,383398] equal(sk_c10,sk_c12).
% 383408 [para:383399.1.1,383363.1.2.1,demod:383195] equal(sk_c11,sk_c12).
% 383414 [para:383402.1.2,383298.1.1.1] equal(inverse(sk_c10),sk_c11).
% 383425 [para:383402.1.2,383408.1.2] equal(sk_c11,sk_c10).
% 383440 [hyper:383198,383414,demod:383397,cut:383425] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 3 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103,383439,50,30104,383439,30,30104,383439,40,30104,383514,0,30104,383714,50,30105,383789,0,30109)
%
%
% START OF PROOF
% 383716 [] equal(multiply(identity,X),X).
% 383717 [] equal(multiply(inverse(X),X),identity).
% 383718 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 383719 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(inverse(X),sk_c12).
% 383728 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 383729 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 383738 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c12).
% 383739 [?] ?
% 383748 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 383749 [] equal(multiply(sk_c2,sk_c3),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 383758 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 383759 [] equal(multiply(sk_c1,sk_c11),sk_c12) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 383768 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 383769 [?] ?
% 383778 [] equal(multiply(sk_c11,sk_c10),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 383779 [] equal(multiply(sk_c11,sk_c10),sk_c12) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 383788 [] equal(inverse(sk_c12),sk_c11) | equal(inverse(sk_c4),sk_c12).
% 383789 [?] ?
% 383797 [hyper:383719,383738,binarycut:383739] equal(inverse(sk_c2),sk_c3).
% 383798 [para:383797.1.1,383717.1.1.1] equal(multiply(sk_c3,sk_c2),identity).
% 383817 [hyper:383719,383768,binarycut:383769] equal(inverse(sk_c1),sk_c12).
% 383823 [para:383817.1.1,383717.1.1.1] equal(multiply(sk_c12,sk_c1),identity).
% 383834 [hyper:383719,383788,binarycut:383789] equal(inverse(sk_c12),sk_c11).
% 383835 [para:383834.1.1,383717.1.1.1] equal(multiply(sk_c11,sk_c12),identity).
% 383868 [hyper:383719,383729,383728] equal(multiply(sk_c3,sk_c12),sk_c11).
% 383890 [hyper:383719,383749,383748] equal(multiply(sk_c2,sk_c3),sk_c11).
% 383897 [hyper:383719,383759,383758] equal(multiply(sk_c1,sk_c11),sk_c12).
% 383904 [hyper:383719,383779,383778] equal(multiply(sk_c11,sk_c10),sk_c12).
% 383905 [para:383717.1.1,383718.1.1.1,demod:383716] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 383906 [para:383798.1.1,383718.1.1.1,demod:383716] equal(X,multiply(sk_c3,multiply(sk_c2,X))).
% 383907 [para:383823.1.1,383718.1.1.1,demod:383716] equal(X,multiply(sk_c12,multiply(sk_c1,X))).
% 383909 [para:383868.1.1,383718.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c3,multiply(sk_c12,X))).
% 383910 [para:383890.1.1,383718.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c2,multiply(sk_c3,X))).
% 383913 [para:383890.1.1,383906.1.2.2] equal(sk_c3,multiply(sk_c3,sk_c11)).
% 383915 [para:383897.1.1,383907.1.2.2] equal(sk_c11,multiply(sk_c12,sk_c12)).
% 383916 [para:383915.1.2,383718.1.1.1] equal(multiply(sk_c11,X),multiply(sk_c12,multiply(sk_c12,X))).
% 383918 [para:383717.1.1,383905.1.2.2] equal(X,multiply(inverse(inverse(X)),identity)).
% 383920 [para:383823.1.1,383905.1.2.2,demod:383834] equal(sk_c1,multiply(sk_c11,identity)).
% 383921 [para:383835.1.1,383905.1.2.2] equal(sk_c12,multiply(inverse(sk_c11),identity)).
% 383924 [para:383904.1.1,383905.1.2.2] equal(sk_c10,multiply(inverse(sk_c11),sk_c12)).
% 383926 [para:383907.1.2,383905.1.2.2,demod:383834] equal(multiply(sk_c1,X),multiply(sk_c11,X)).
% 383928 [para:383920.1.2,383905.1.2.2] equal(identity,multiply(inverse(sk_c11),sk_c1)).
% 383929 [para:383921.1.2,383718.1.1.1,demod:383716] equal(multiply(sk_c12,X),multiply(inverse(sk_c11),X)).
% 383931 [para:383924.1.2,383718.1.1.1,demod:383926,383916,383929] equal(multiply(sk_c10,X),multiply(sk_c1,X)).
% 383933 [para:383928.1.2,383905.1.2.2,demod:383918] equal(sk_c1,sk_c11).
% 383934 [para:383933.1.2,383835.1.1.1,demod:383931] equal(multiply(sk_c10,sk_c12),identity).
% 383942 [para:383933.1.2,383924.1.2.1.1,demod:383915,383817] equal(sk_c10,sk_c11).
% 383948 [para:383942.1.2,383933.1.2] equal(sk_c1,sk_c10).
% 383950 [para:383948.1.1,383817.1.1.1] equal(inverse(sk_c10),sk_c12).
% 383955 [para:383915.1.2,383909.1.2.2,demod:383913,383835] equal(identity,sk_c3).
% 383960 [para:383955.1.2,383906.1.2.1,demod:383716] equal(X,multiply(sk_c2,X)).
% 383979 [para:383868.1.1,383910.1.2.2,demod:383960,383835] equal(identity,sk_c11).
% 384016 [hyper:383719,383950,demod:383934,cut:383979] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 4 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103,383439,50,30104,383439,30,30104,383439,40,30104,383514,0,30104,383714,50,30105,383789,0,30109,384015,50,30110,384015,30,30110,384015,40,30110,384090,0,30110)
%
%
% START OF PROOF
% 384017 [] equal(multiply(identity,X),X).
% 384018 [] equal(multiply(inverse(X),X),identity).
% 384019 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 384020 [] -equal(multiply(X,sk_c12),sk_c11) | -equal(multiply(Y,X),sk_c11) | -equal(inverse(Y),X).
% 384022 [?] ?
% 384023 [?] ?
% 384025 [?] ?
% 384026 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c6,sk_c9),sk_c12).
% 384029 [?] ?
% 384030 [] equal(multiply(sk_c3,sk_c12),sk_c11) | equal(multiply(sk_c4,sk_c12),sk_c11).
% 384032 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c7),sk_c9).
% 384033 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c8),sk_c7).
% 384035 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c6),sk_c9).
% 384036 [] equal(multiply(sk_c6,sk_c9),sk_c12) | equal(inverse(sk_c2),sk_c3).
% 384039 [] equal(inverse(sk_c2),sk_c3) | equal(inverse(sk_c4),sk_c12).
% 384040 [] equal(multiply(sk_c4,sk_c12),sk_c11) | equal(inverse(sk_c2),sk_c3).
% 384042 [?] ?
% 384043 [?] ?
% 384045 [?] ?
% 384046 [?] ?
% 384049 [?] ?
% 384050 [?] ?
% 384095 [hyper:384020,384032,binarycut:384042,binarycut:384022] equal(inverse(sk_c7),sk_c9).
% 384098 [para:384095.1.1,384018.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 384102 [hyper:384020,384033,binarycut:384043,binarycut:384023] equal(inverse(sk_c8),sk_c7).
% 384106 [para:384102.1.1,384018.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 384110 [hyper:384020,384035,binarycut:384045,binarycut:384025] equal(inverse(sk_c6),sk_c9).
% 384119 [para:384110.1.1,384018.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 384136 [hyper:384020,384039,binarycut:384049,binarycut:384029] equal(inverse(sk_c4),sk_c12).
% 384142 [para:384136.1.1,384018.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 384162 [hyper:384020,384036,binarycut:384046,binarycut:384026] equal(multiply(sk_c6,sk_c9),sk_c12).
% 384179 [hyper:384020,384040,binarycut:384050,binarycut:384030] equal(multiply(sk_c4,sk_c12),sk_c11).
% 384186 [para:384018.1.1,384019.1.1.1,demod:384017] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 384187 [para:384098.1.1,384019.1.1.1,demod:384017] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 384188 [para:384106.1.1,384019.1.1.1,demod:384017] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 384194 [para:384162.1.1,384019.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 384199 [para:384106.1.1,384187.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 384200 [para:384199.1.2,384019.1.1.1,demod:384017] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 384208 [para:384098.1.1,384186.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),identity)).
% 384210 [para:384119.1.1,384186.1.2.2,demod:384208] equal(sk_c6,sk_c7).
% 384219 [para:384210.1.2,384188.1.2.1,demod:384194,384200] equal(X,multiply(sk_c12,X)).
% 384224 [para:384219.1.2,384142.1.1] equal(sk_c4,identity).
% 384226 [para:384224.1.1,384136.1.1.1] equal(inverse(identity),sk_c12).
% 384227 [para:384224.1.1,384179.1.1.1,demod:384017] equal(sk_c12,sk_c11).
% 384231 [hyper:384020,384226,demod:384219,384017,cut:384227,cut:384227] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% Split component 5 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103,383439,50,30104,383439,30,30104,383439,40,30104,383514,0,30104,383714,50,30105,383789,0,30109,384015,50,30110,384015,30,30110,384015,40,30110,384090,0,30110,384230,50,30110,384230,30,30110,384230,40,30110,384305,0,30115,384514,50,30116,384589,0,30116)
%
%
% START OF PROOF
% 384445 [?] ?
% 384516 [] equal(multiply(identity,X),X).
% 384517 [] equal(multiply(inverse(X),X),identity).
% 384518 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 384519 [] -equal(multiply(X,sk_c11),sk_c12) | -equal(inverse(X),sk_c12).
% 384551 [?] ?
% 384552 [?] ?
% 384554 [?] ?
% 384555 [?] ?
% 384558 [?] ?
% 384561 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c7),sk_c9).
% 384562 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c8),sk_c7).
% 384564 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c6),sk_c9).
% 384565 [] equal(multiply(sk_c6,sk_c9),sk_c12) | equal(inverse(sk_c1),sk_c12).
% 384568 [] equal(inverse(sk_c1),sk_c12) | equal(inverse(sk_c4),sk_c12).
% 384600 [hyper:384519,384561,binarycut:384551] equal(inverse(sk_c7),sk_c9).
% 384601 [para:384600.1.1,384517.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 384605 [hyper:384519,384562,binarycut:384552] equal(inverse(sk_c8),sk_c7).
% 384606 [para:384605.1.1,384517.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 384612 [hyper:384519,384564,binarycut:384554] equal(inverse(sk_c6),sk_c9).
% 384613 [para:384612.1.1,384517.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 384621 [hyper:384519,384568,binarycut:384558] equal(inverse(sk_c4),sk_c12).
% 384626 [para:384621.1.1,384517.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 384650 [hyper:384519,384565,binarycut:384555] equal(multiply(sk_c6,sk_c9),sk_c12).
% 384657 [para:384517.1.1,384518.1.1.1,demod:384516] equal(X,multiply(inverse(Y),multiply(Y,X))).
% 384658 [para:384601.1.1,384518.1.1.1,demod:384516] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 384659 [para:384606.1.1,384518.1.1.1,demod:384516] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 384665 [para:384650.1.1,384518.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 384668 [para:384606.1.1,384658.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 384669 [para:384668.1.2,384518.1.1.1,demod:384516] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 384677 [para:384601.1.1,384657.1.2.2] equal(sk_c7,multiply(inverse(sk_c9),identity)).
% 384679 [para:384613.1.1,384657.1.2.2,demod:384677] equal(sk_c6,sk_c7).
% 384690 [para:384679.1.2,384659.1.2.1,demod:384665,384669] equal(X,multiply(sk_c12,X)).
% 384693 [para:384690.1.2,384626.1.1] equal(sk_c4,identity).
% 384695 [para:384693.1.1,384621.1.1.1] equal(inverse(identity),sk_c12).
% 384700 [hyper:384519,384695,demod:384516,cut:384445] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% Split component 6 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(inverse(sk_c12),sk_c11).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103,383439,50,30104,383439,30,30104,383439,40,30104,383514,0,30104,383714,50,30105,383789,0,30109,384015,50,30110,384015,30,30110,384015,40,30110,384090,0,30110,384230,50,30110,384230,30,30110,384230,40,30110,384305,0,30115,384514,50,30116,384589,0,30116,384699,50,30116,384699,30,30116,384699,40,30116,384774,0,30121,384998,50,30123,385073,0,30123,385360,50,30129,385435,0,30133,385730,50,30140,385805,0,30140,386108,50,30150,386183,0,30154,386492,50,30167,386567,0,30167,386884,50,30189,386959,0,30193,387284,50,30230,387359,0,30230,387694,50,30302,387769,0,30302,388114,50,30434,388114,40,30434,388189,0,30434)
%
%
% START OF PROOF
% 388116 [] equal(multiply(identity,X),X).
% 388117 [] equal(multiply(inverse(X),X),identity).
% 388118 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 388119 [] -equal(inverse(sk_c12),sk_c11).
% 388180 [?] ?
% 388181 [?] ?
% 388182 [?] ?
% 388183 [?] ?
% 388184 [?] ?
% 388185 [?] ?
% 388186 [?] ?
% 388187 [?] ?
% 388188 [?] ?
% 388189 [?] ?
% 388223 [input:388181,cut:388119] equal(inverse(sk_c7),sk_c9).
% 388224 [para:388223.1.1,388117.1.1.1] equal(multiply(sk_c9,sk_c7),identity).
% 388227 [input:388182,cut:388119] equal(inverse(sk_c8),sk_c7).
% 388228 [para:388227.1.1,388117.1.1.1] equal(multiply(sk_c7,sk_c8),identity).
% 388229 [input:388184,cut:388119] equal(inverse(sk_c6),sk_c9).
% 388230 [para:388229.1.1,388117.1.1.1] equal(multiply(sk_c9,sk_c6),identity).
% 388232 [input:388186,cut:388119] equal(inverse(sk_c5),sk_c11).
% 388233 [para:388232.1.1,388117.1.1.1] equal(multiply(sk_c11,sk_c5),identity).
% 388234 [input:388188,cut:388119] equal(inverse(sk_c4),sk_c12).
% 388235 [para:388234.1.1,388117.1.1.1] equal(multiply(sk_c12,sk_c4),identity).
% 388281 [input:388180,cut:388119] equal(multiply(sk_c8,sk_c9),sk_c7).
% 388282 [input:388183,cut:388119] equal(multiply(sk_c9,sk_c11),sk_c12).
% 388284 [input:388185,cut:388119] equal(multiply(sk_c6,sk_c9),sk_c12).
% 388285 [input:388187,cut:388119] equal(multiply(sk_c5,sk_c11),sk_c10).
% 388286 [input:388189,cut:388119] equal(multiply(sk_c4,sk_c12),sk_c11).
% 388312 [para:388224.1.1,388118.1.1.1,demod:388116] equal(X,multiply(sk_c9,multiply(sk_c7,X))).
% 388313 [para:388228.1.1,388118.1.1.1,demod:388116] equal(X,multiply(sk_c7,multiply(sk_c8,X))).
% 388314 [para:388230.1.1,388118.1.1.1,demod:388116] equal(X,multiply(sk_c9,multiply(sk_c6,X))).
% 388317 [para:388233.1.1,388118.1.1.1,demod:388116] equal(X,multiply(sk_c11,multiply(sk_c5,X))).
% 388318 [para:388235.1.1,388118.1.1.1,demod:388116] equal(X,multiply(sk_c12,multiply(sk_c4,X))).
% 388365 [para:388284.1.1,388118.1.1.1] equal(multiply(sk_c12,X),multiply(sk_c6,multiply(sk_c9,X))).
% 388388 [para:388228.1.1,388312.1.2.2] equal(sk_c8,multiply(sk_c9,identity)).
% 388389 [para:388388.1.2,388118.1.1.1,demod:388116] equal(multiply(sk_c8,X),multiply(sk_c9,X)).
% 388394 [para:388281.1.1,388313.1.2.2] equal(sk_c9,multiply(sk_c7,sk_c7)).
% 388397 [para:388394.1.2,388312.1.2.2] equal(sk_c7,multiply(sk_c9,sk_c9)).
% 388404 [para:388284.1.1,388314.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c12)).
% 388410 [para:388285.1.1,388317.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 388425 [para:388286.1.1,388318.1.2.2] equal(sk_c12,multiply(sk_c12,sk_c11)).
% 388429 [para:388389.1.1,388313.1.2.2] equal(X,multiply(sk_c7,multiply(sk_c9,X))).
% 388430 [para:388224.1.1,388429.1.2.2] equal(sk_c7,multiply(sk_c7,identity)).
% 388431 [para:388230.1.1,388429.1.2.2,demod:388430] equal(sk_c6,sk_c7).
% 388441 [para:388431.1.2,388313.1.2.1,demod:388365,388389] equal(X,multiply(sk_c12,X)).
% 388450 [para:388441.1.2,388318.1.2] equal(X,multiply(sk_c4,X)).
% 388451 [para:388441.1.2,388425.1.2] equal(sk_c12,sk_c11).
% 388468 [para:388451.1.1,388404.1.2.2] equal(sk_c9,multiply(sk_c9,sk_c11)).
% 388469 [para:388451.1.1,388318.1.2.1,demod:388450] equal(X,multiply(sk_c11,X)).
% 388482 [para:388469.1.2,388410.1.2] equal(sk_c11,sk_c10).
% 388498 [para:388482.1.1,388282.1.1.2] equal(multiply(sk_c9,sk_c10),sk_c12).
% 388502 [para:388482.1.1,388425.1.2.2,demod:388441] equal(sk_c12,sk_c10).
% 388511 [para:388502.1.1,388404.1.2.2,demod:388498] equal(sk_c9,sk_c12).
% 388522 [para:388511.1.2,388286.1.1.2,demod:388450] equal(sk_c9,sk_c11).
% 388527 [para:388511.1.2,388404.1.2.2,demod:388397] equal(sk_c9,sk_c7).
% 388529 [para:388511.1.2,388425.1.2.1,demod:388468] equal(sk_c12,sk_c9).
% 388547 [para:388527.1.2,388223.1.1.1] equal(inverse(sk_c9),sk_c9).
% 388555 [para:388529.1.1,388119.1.1.1,demod:388547,cut:388522] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split component 7 started.
%
% START OF PROOFPART
% Making new sos for split:
% Original clause to be split:
% -equal(inverse(sk_c12),sk_c11) | -equal(multiply(sk_c11,sk_c10),sk_c12) | -equal(inverse(X),sk_c12) | -equal(multiply(X,sk_c11),sk_c12) | -equal(multiply(Y,Z),sk_c11) | -equal(inverse(Y),Z) | -equal(multiply(Z,sk_c12),sk_c11) | -equal(multiply(U,sk_c12),sk_c11) | -equal(inverse(U),sk_c12) | -equal(multiply(V,sk_c11),sk_c10) | -equal(inverse(V),sk_c11) | -equal(multiply(W,X1),sk_c12) | -equal(inverse(W),X1) | -equal(multiply(X1,sk_c11),sk_c12) | -equal(inverse(X2),X3) | -equal(inverse(X3),X1) | -equal(multiply(X2,X1),X3).
% Split part used next: -equal(multiply(sk_c11,sk_c10),sk_c12).
% END OF PROOFPART
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 3
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 4
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 5
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 6
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 7
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 8
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 9
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 10
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using hyperresolution
% not using sos strategy
% using positive unit paramodulation strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% clause length limited to 33
% clause depth limited to 11
% seconds given: 4
%
%
% proof attempt stopped: sos exhausted
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% ********* EMPTY CLAUSE DERIVED *********
%
%
% timer checkpoints: c(75,40,1,159,0,1,161756,5,1502,161756,1,1502,161756,50,1502,161756,40,1502,161840,0,1502,162160,5,2113,162162,1,2116,162162,50,2116,162162,40,2116,162246,0,2116,162622,5,2737,162632,1,2739,162632,50,2739,162632,40,2739,162716,0,2740,183978,3,4241,185157,4,4991,186498,1,5741,186498,50,5741,186498,40,5741,186582,0,5741,200842,3,6492,201716,4,6867,202414,1,7242,202414,50,7242,202414,40,7242,202498,0,7242,203079,5,8745,203085,1,8745,203085,50,8745,203085,40,8745,203169,0,8745,263465,3,12651,264495,4,14596,265453,5,16546,265454,1,16546,265454,50,16549,265454,40,16549,265538,0,16549,303792,3,19100,304860,4,20375,305600,1,21650,305600,50,21651,305600,40,21651,305684,0,21651,335586,3,23152,336382,4,23902,337223,5,24652,337224,1,24652,337224,50,24653,337224,40,24653,337308,0,24653,337903,5,26189,337908,1,26189,337908,50,26189,337908,40,26189,337992,0,26189,361572,3,27390,362149,4,27990,362864,1,28590,362864,50,28590,362864,40,28590,362948,0,28590,379794,3,29341,380378,4,29716,380833,1,30091,380833,50,30091,380833,40,30091,380833,40,30091,380982,0,30092,383193,50,30103,383193,30,30103,383193,40,30103,383268,0,30103,383439,50,30104,383439,30,30104,383439,40,30104,383514,0,30104,383714,50,30105,383789,0,30109,384015,50,30110,384015,30,30110,384015,40,30110,384090,0,30110,384230,50,30110,384230,30,30110,384230,40,30110,384305,0,30115,384514,50,30116,384589,0,30116,384699,50,30116,384699,30,30116,384699,40,30116,384774,0,30121,384998,50,30123,385073,0,30123,385360,50,30129,385435,0,30133,385730,50,30140,385805,0,30140,386108,50,30150,386183,0,30154,386492,50,30167,386567,0,30167,386884,50,30189,386959,0,30193,387284,50,30230,387359,0,30230,387694,50,30302,387769,0,30302,388114,50,30434,388114,40,30434,388189,0,30434,388554,50,30435,388554,30,30435,388554,40,30435,388629,0,30436,388853,50,30438,388928,0,30442,389215,50,30447,389290,0,30447,389585,50,30454,389660,0,30458,389963,50,30467,390038,0,30467,390347,50,30480,390422,0,30485,390739,50,30506,390814,0,30506,391139,50,30543,391214,0,30547,391549,50,30616,391624,0,30616,391969,50,30752,391969,40,30752,392044,0,30752)
%
%
% START OF PROOF
% 391762 [?] ?
% 391971 [] equal(multiply(identity,X),X).
% 391972 [] equal(multiply(inverse(X),X),identity).
% 391973 [] equal(multiply(multiply(X,Y),Z),multiply(X,multiply(Y,Z))).
% 391974 [] -equal(multiply(sk_c11,sk_c10),sk_c12).
% 392031 [?] ?
% 392032 [?] ?
% 392154 [input:392031,cut:391974] equal(inverse(sk_c5),sk_c11).
% 392155 [para:392154.1.1,391972.1.1.1] equal(multiply(sk_c11,sk_c5),identity).
% 392193 [input:392032,cut:391974] equal(multiply(sk_c5,sk_c11),sk_c10).
% 392242 [para:392155.1.1,391973.1.1.1,demod:391971] equal(X,multiply(sk_c11,multiply(sk_c5,X))).
% 392308 [para:392193.1.1,392242.1.2.2] equal(sk_c11,multiply(sk_c11,sk_c10)).
% 392309 [para:392308.1.2,391974.1.1,cut:391762] contradiction
% END OF PROOF
%
% Proof found by the following strategy:
%
% using binary resolution
% not using sos strategy
% using unit strategy
% using dynamic demodulation
% using ordered paramodulation
% using kb ordering for equality
% preferring bigger arities for lex ordering
% using clause demodulation
% seconds given: 2
%
%
% Split attempt finished with SUCCESS.
%
% ***GANDALF_FOUND_A_REFUTATION***
%
% Global statistics over all passes:
%
% given clauses: 35435
% derived clauses: 3189754
% kept clauses: 187165
% kept size sum: 254069
% kept mid-nuclei: 130787
% kept new demods: 5305
% forw unit-subs: 830298
% forw double-subs: 1798591
% forw overdouble-subs: 173827
% backward subs: 20989
% fast unit cutoff: 28241
% full unit cutoff: 0
% dbl unit cutoff: 38942
% real runtime : 308.94
% process. runtime: 307.52
% specific non-discr-tree subsumption statistics:
% tried: 18280298
% length fails: 3237107
% strength fails: 4035188
% predlist fails: 440874
% aux str. fails: 1126824
% by-lit fails: 2912001
% full subs tried: 3592560
% full subs fail: 3533375
%
% ; program args: ("/home/graph/tptp/Systems/Gandalf---c-2.6/gandalf" "-time" "600" "/home/graph/tptp/TSTP/PreparedTPTP/otter:hypothesis:set(auto),clear(print_given)---add_equality:r/GRP/GRP382-1+eq_r.in")
%
%------------------------------------------------------------------------------